We consider multiphysics applications from algorithmic and architectural perspectives,
where “algorithmic” includes both mathematical analysis and computational complexity, and …

This text presents a comprehensive mathematical theory for elliptic, parabolic, and
hyperbolic differential equations. It compares finite element and finite difference methods …

These notes serve as an introduction to a subject of study in computational mathematics
referred to as domain decomposition methods. It concerns divide and conquer methods for …

Like many problems in biofluid mechanics, cardiac mechanics can be modeled as the
dynamic interaction of a viscous incompressible fluid (the blood) and a (visco-) elastic …

Derivation, stability, and error analysis in both discrete H^1-and L^2-norms for cell-centered
finite volume approximations of convection-diffusion problems are presented. Various …

Two cell‐centered finite difference schemes on Voronoi meshes are derived and
investigated. Stability and error estimates in a discrete H1‐norm for both symmetric and …

In this paper we develop an OcTree discretization for Maxwell's equations in the quasi-static
regime. We then use this discretization in order to develop a multigrid method for Maxwell's …

Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
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New mimetic discretizations of diffusion-type equations (for instance, equations modeling
single phase Darcy flow in porous media) on unstructured polygonal meshes are derived …

Optimization in Solving Elliptic Problems focuses on one of the most interesting and
challenging problems of computational mathematics-the optimization of numerical …